Finite Group Databasebeta

← #13263487

Subgroups — #13263487

Order 1792.

424 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2487C211yesmaximal, characteristic
2#11729356C211yesmaximal, characteristic
3#11729355C211yesmaximal, characteristic
4#11725442C214yesmaximal, complemented
5C2×C4×C7×D4C2211yescharacteristic
6C22×C7×C4⋊C4C411yescharacteristic
7C7×#400—21no—
8C7×#399—21no—
9C7×#389—21no—
10C7×#386C412yes—
11C7×#385C2212yes—
12C7×#380—21no—
13C7×#380C411yescharacteristic
14#89979—21no—
15#89697—21no—
16#89323—21no—
17#89320—21no—
18#89320C2212yes—
19#89320C2212yes—
20#11579—71nomaximal, Sylow
21C22×C7×D4C2×C411yescharacteristic
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7C2×C412yes—
24C23×C4×C7D411yescharacteristic
25C4×C7×D4—41no—
26C4×C7×D4—41no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—22no—
31C2×C7×C4⋊C4—41no—
32C2×C7×C4⋊C4—41no—
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C7×C22⋊C4—22no—
35C2×C7×C22⋊C4C2×C412yes—
36C2×C7×C22⋊C4D411yescharacteristic
37C2×C7×C22⋊C4C2311yescharacteristic
38C2×C42×C7D411yescharacteristic
39C2×#1136—41no—
40C7×#95—21no—
41C7×#95—22no—
42C7×#95—22no—
43C22⋊(C7⋊C8)—22no—
44C22⋊(C7⋊C8)—22no—
45C22⋊(C7⋊C8)—41no—
46C4⋊(C7⋊C8)—41no—
47C4×C7⋊C8—41no—
48#2487D711yescharacteristic
49#1465—71no—
50#1460—71no—
51#1326—74no—
52C24×C7C22⋊C411yescharacteristic
53C24×C7C22×C411yescharacteristic
54C2×C7×D4—22no—
55C2×C7×D4—22no—
56C2×C7×D4—41no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7—42no—
64C22×C4×C7—42no—
65C22×C4×C7—42no—
66C22×C4×C7—82no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C7×C4⋊C4—41no—
73C7×C4⋊C4—42no—
74C7×C4⋊C4—42no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—41no—
77C7×C4⋊C4—82no—
78C7×C22⋊C4—24no—
79C7×C22⋊C4—41no—
80C7×C22⋊C4—41no—
81C7×C22⋊C4—82no—
82C42×C7—21no—
83C42×C7—21no—
84#1136—82no—
85C2×C7⋊C8—42no—
86C2×C7⋊C8—42no—
87C2×C4×D4C2×D711yescharacteristic
88C22×C4⋊C4Dic711yescharacteristic
89#431—141no—
90#407—141no—
91#400—21no—
92#399—21no—
93#389—21no—
94#386Dic712yes—
95#385C2×D712yes—
96#380—21no—
97#380Dic711yescharacteristic
98#324—141no—
99#323—72no—
100#323—72no—
101#323—141no—
102C23×C7—21no—
103C23×C7—21no—
104C23×C7—21no—
105C23×C7—21no—
106C23×C7—21no—
107C23×C7—41no—
108C23×C7—41no—
109C23×C7—41no—
110C23×C7—41no—
111C23×C7C2×C22⋊C411yescharacteristic
112C23×C7#13112yes—
113C7×D4—44no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—22no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—42no—
121C2×C4×C7—42no—
122C2×C4×C7—42no—
123C2×C4×C7—41no—
124C2×C4×C7—41no—
125C2×C4×C7—41no—
126C2×C4×C7—42no—
127C2×C4×C7—42no—
128C2×C4×C7—42no—
129C2×C4×C7—42no—
130C2×C4×C7—42no—
131C2×C4×C7—42no—
132C2×C4×C7—81no—
133C2×C4×C7—84no—
134C2×C4×C7#9911yescharacteristic
135C2×C4×C7#9911yescharacteristic
136C2×C4×C7#10112yes—
137C7⋊C8—82no—
138C7⋊C8—82no—
139C22×D4C2×Dic711yescharacteristic
140C23×C4C2×Dic711yescharacteristic
141C23×C4C2×Dic712yes—
142C23×C4C22⋊D711yescharacteristic
143C2×M16—281no—
144C4×D4—41no—
145C4×D4—41no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4C22⋊D711yescharacteristic
153C2×C22⋊C4—22no—
154C2×C22⋊C4C2×Dic712yes—
155C2×C22⋊C4C22⋊D711yescharacteristic
156C2×C22⋊C4C22×D711yescharacteristic
157C2×C42C22⋊D711yescharacteristic
158C4⋊C8—281no—
159C22⋊C8—142no—
160C22⋊C8—142no—
161C22⋊C8—281no—
162C4×C8—281no—
163#95—21no—
164#95—22no—
165#95—22no—
166C22×C7—21no—
167C22×C7—21no—
168C22×C7—22no—
169C22×C7—42no—
170C22×C7—42no—
171C22×C7—42no—
172C22×C7—41no—
173C22×C7—41no—
174C22×C7—41no—
175C22×C7—41no—
176C22×C7—41no—
177C22×C7—81no—
178C22×C7#40811yescharacteristic
179C22×C7C2×#9911yescharacteristic
180C22×C7C2×#10111yescharacteristic
181C4×C7—21no—
182C4×C7—22no—
183C4×C7—41no—
184C4×C7—41no—
185C4×C7—41no—
186C4×C7—82no—
187C4×C7—82no—
188C4×C7#35212yes—
189C24C22⋊Dic711yescharacteristic
190C24C22×Dic711yescharacteristic
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—82no—
204C22×C4C22⋊Dic711yescharacteristic
205C22×C4C22⋊Dic711yescharacteristic
206C22×C4C22⋊Dic711yescharacteristic
207C22×C4C2×C22⋊D711yescharacteristic
208C22×C4C2×C22⋊D711yescharacteristic
209M16—562no—
210C2×C8—282no—
211C2×C8—282no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—82no—
218C22⋊C4—24no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—82no—
222C42—21no—
223C42—21no—
224C2×C7—21no—
225C2×C7—21no—
226C2×C7—42no—
227C2×C7—81no—
228C2×C7#147211yescharacteristic
229C2×C7C2×#35211yescharacteristic
230C2×C7#212211yescharacteristic
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23#651112yes—
241C23C2×C22⋊Dic711yescharacteristic
242D4—44no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—81no—
262C2×C4—84no—
263C2×C4#640811yescharacteristic
264C2×C4#640811yescharacteristic
265C2×C4#641012yes—
266C8—562no—
267C8—562no—
268C7#1157911yescharacteristic, complemented, Sylow
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22C2×#640811yescharacteristic
282C22C2×#641011yescharacteristic
283C22#9000611yescharacteristic
284C4—22no—
285C4—21no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—82no—
290C4—82no—
291C4#8933412yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—81no—
296C2#1172944511yescharacteristic
297C2C2×#8933411yescharacteristic
298C2#1172961311yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC24×C7C22×C4
FrattiniC2×C22⋊C4C22×D7
FittingC7×#2487C2
socleC22×C7C2×#99
prime radicalC22×C7×D4C2×C4
cosocleC2×C7×C22⋊C4C23
hypercenter#2487D7
hypocenterC7#11579
LCSG ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #11725442C2semidirect
268. C7#11579semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C7×#24872
#117293562
#117293552
#117254422
#115797